Space of modular forms of level 2112, weight 4, and trivial character

• Label: 2112.4.a
• Level: $2112$
• Weight: $4$
• Character orbit: 2112.a
• Rep. character: $\chi_{2112}(1,\cdot)$
• Character field: $\Q$
• Dimension: $120$
• Newform subspaces: $58$
• Sturm bound: $1536$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2112 = 2^{6} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2112.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 58 \)
Sturm bound:			\(1536\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2112))\).

	Total	New	Old
Modular forms	1176	120	1056
Cusp forms	1128	120	1008
Eisenstein series	48	0	48

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	\(11\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(152\)	\(16\)	\(136\)		\(146\)	\(16\)	\(130\)		\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(-\)	\(-\)		\(142\)	\(14\)	\(128\)		\(136\)	\(14\)	\(122\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(148\)	\(15\)	\(133\)		\(142\)	\(15\)	\(127\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(146\)	\(17\)	\(129\)		\(140\)	\(17\)	\(123\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(142\)	\(14\)	\(128\)		\(136\)	\(14\)	\(122\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(152\)	\(16\)	\(136\)		\(146\)	\(16\)	\(130\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(146\)	\(15\)	\(131\)		\(140\)	\(15\)	\(125\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(148\)	\(13\)	\(135\)		\(142\)	\(13\)	\(129\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(596\)	\(64\)	\(532\)		\(572\)	\(64\)	\(508\)		\(24\)	\(0\)	\(24\)
Minus space			\(-\)		\(580\)	\(56\)	\(524\)		\(556\)	\(56\)	\(500\)		\(24\)	\(0\)	\(24\)

Trace form

120 * q + 1080 * q^9 + 144 * q^13 - 208 * q^17 - 240 * q^21 + 3176 * q^25 - 1008 * q^37 + 944 * q^41 + 5880 * q^49 - 3984 * q^61 + 3072 * q^65 - 1056 * q^69 + 592 * q^73 + 9720 * q^81 + 480 * q^85 - 176 * q^89 - 3696 * q^93 + 3632 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2112))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	11
2112.4.a.a	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				132.4.a.c	$1$	$0$	\(0\)	\(-3\)	\(-22\)	\(20\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-22q^{5}+20q^{7}+9q^{9}+11q^{11}+\cdots\)
2112.4.a.b	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				1056.4.a.a	$1$	$1$	\(0\)	\(-3\)	\(-14\)	\(34\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-14q^{5}+34q^{7}+9q^{9}-11q^{11}+\cdots\)
2112.4.a.c	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				264.4.a.b	$1$	$0$	\(0\)	\(-3\)	\(-12\)	\(-22\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-12q^{5}-22q^{7}+9q^{9}+11q^{11}+\cdots\)
2112.4.a.d	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				66.4.a.b	$1$	$0$	\(0\)	\(-3\)	\(-10\)	\(-16\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-10q^{5}-2^{4}q^{7}+9q^{9}+11q^{11}+\cdots\)
2112.4.a.e	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				132.4.a.d	$1$	$1$	\(0\)	\(-3\)	\(-10\)	\(8\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-10q^{5}+8q^{7}+9q^{9}+11q^{11}+\cdots\)
2112.4.a.f	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				132.4.a.b	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-2q^{7}+9q^{9}-11q^{11}+88q^{13}+\cdots\)
2112.4.a.g	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				66.4.a.a	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(14\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+14q^{7}+9q^{9}-11q^{11}-80q^{13}+\cdots\)
2112.4.a.h	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				33.4.a.b	$1$	$0$	\(0\)	\(-3\)	\(4\)	\(26\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+4q^{5}+26q^{7}+9q^{9}+11q^{11}+\cdots\)
2112.4.a.i	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				264.4.a.c	$1$	$0$	\(0\)	\(-3\)	\(6\)	\(-14\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+6q^{5}-14q^{7}+9q^{9}-11q^{11}+\cdots\)
2112.4.a.j	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				264.4.a.d	$1$	$1$	\(0\)	\(-3\)	\(6\)	\(-8\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+6q^{5}-8q^{7}+9q^{9}+11q^{11}+\cdots\)
2112.4.a.k	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				132.4.a.a	$1$	$0$	\(0\)	\(-3\)	\(12\)	\(-14\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+12q^{5}-14q^{7}+9q^{9}+11q^{11}+\cdots\)
2112.4.a.l	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				33.4.a.a	$1$	$1$	\(0\)	\(-3\)	\(14\)	\(-32\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+14q^{5}-2^{5}q^{7}+9q^{9}+11q^{11}+\cdots\)
2112.4.a.m	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				264.4.a.a	$1$	$0$	\(0\)	\(-3\)	\(18\)	\(28\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+18q^{5}+28q^{7}+9q^{9}+11q^{11}+\cdots\)
2112.4.a.n	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				132.4.a.c	$1$	$1$	\(0\)	\(3\)	\(-22\)	\(-20\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-22q^{5}-20q^{7}+9q^{9}-11q^{11}+\cdots\)
2112.4.a.o	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				1056.4.a.a	$1$	$1$	\(0\)	\(3\)	\(-14\)	\(-34\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-14q^{5}-34q^{7}+9q^{9}+11q^{11}+\cdots\)
2112.4.a.p	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				264.4.a.b	$1$	$1$	\(0\)	\(3\)	\(-12\)	\(22\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-12q^{5}+22q^{7}+9q^{9}-11q^{11}+\cdots\)
2112.4.a.q	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				132.4.a.d	$1$	$0$	\(0\)	\(3\)	\(-10\)	\(-8\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-10q^{5}-8q^{7}+9q^{9}-11q^{11}+\cdots\)
2112.4.a.r	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				66.4.a.b	$1$	$1$	\(0\)	\(3\)	\(-10\)	\(16\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-10q^{5}+2^{4}q^{7}+9q^{9}-11q^{11}+\cdots\)
2112.4.a.s	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				66.4.a.a	$1$	$1$	\(0\)	\(3\)	\(0\)	\(-14\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-14q^{7}+9q^{9}+11q^{11}-80q^{13}+\cdots\)
2112.4.a.t	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				132.4.a.b	$1$	$0$	\(0\)	\(3\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+2q^{7}+9q^{9}+11q^{11}+88q^{13}+\cdots\)
2112.4.a.u	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				33.4.a.b	$1$	$1$	\(0\)	\(3\)	\(4\)	\(-26\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+4q^{5}-26q^{7}+9q^{9}-11q^{11}+\cdots\)
2112.4.a.v	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				264.4.a.d	$1$	$0$	\(0\)	\(3\)	\(6\)	\(8\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+6q^{5}+8q^{7}+9q^{9}-11q^{11}+\cdots\)
2112.4.a.w	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				264.4.a.c	$1$	$1$	\(0\)	\(3\)	\(6\)	\(14\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+6q^{5}+14q^{7}+9q^{9}+11q^{11}+\cdots\)
2112.4.a.x	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				132.4.a.a	$1$	$1$	\(0\)	\(3\)	\(12\)	\(14\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+12q^{5}+14q^{7}+9q^{9}-11q^{11}+\cdots\)
2112.4.a.y	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				33.4.a.a	$1$	$0$	\(0\)	\(3\)	\(14\)	\(32\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+14q^{5}+2^{5}q^{7}+9q^{9}-11q^{11}+\cdots\)
2112.4.a.z	$2112$	$4$	2112.a	1.a	$1$	$1$	$1$	$124.612$	\(\Q\)	None	✓				264.4.a.a	$1$	$1$	\(0\)	\(3\)	\(18\)	\(-28\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+18q^{5}-28q^{7}+9q^{9}-11q^{11}+\cdots\)
2112.4.a.ba	$2112$	$4$	2112.a	1.a	$1$	$2$	$2$	$124.612$	\(\Q(\sqrt{33}) \)	None	✓				33.4.a.d	$1$	$0$	\(0\)	\(-6\)	\(-16\)	\(2\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-3q^{3}+(-8-2\beta )q^{5}+(1+\beta )q^{7}+\cdots\)
2112.4.a.bb	$2112$	$4$	2112.a	1.a	$1$	$2$	$2$	$124.612$	\(\Q(\sqrt{97}) \)	None	✓				66.4.a.c	$1$	$1$	\(0\)	\(-6\)	\(-10\)	\(-2\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-3q^{3}+(-5-\beta )q^{5}+(-1-3\beta )q^{7}+\cdots\)
2112.4.a.bc	$2112$	$4$	2112.a	1.a	$1$	$2$	$2$	$124.612$	\(\Q(\sqrt{73}) \)	None	✓				1056.4.a.c	$1$	$1$	\(0\)	\(-6\)	\(-6\)	\(-16\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-3q^{3}+(-3-\beta )q^{5}+(-8-2\beta )q^{7}+\cdots\)
2112.4.a.bd	$2112$	$4$	2112.a	1.a	$1$	$2$	$2$	$124.612$	\(\Q(\sqrt{137}) \)	None	✓				264.4.a.f	$1$	$1$	\(0\)	\(-6\)	\(6\)	\(-16\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-3q^{3}+(3+\beta )q^{5}+(-8-2\beta )q^{7}+\cdots\)
2112.4.a.be	$2112$	$4$	2112.a	1.a	$1$	$2$	$2$	$124.612$	\(\Q(\sqrt{17}) \)	None	✓				264.4.a.e	$1$	$0$	\(0\)	\(-6\)	\(6\)	\(-10\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-3q^{3}+(3+\beta )q^{5}+(-5-\beta )q^{7}+9q^{9}+\cdots\)
2112.4.a.bf	$2112$	$4$	2112.a	1.a	$1$	$2$	$2$	$124.612$	\(\Q(\sqrt{185}) \)	None	✓				264.4.a.g	$1$	$1$	\(0\)	\(-6\)	\(6\)	\(22\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-3q^{3}+(3+\beta )q^{5}+(11-\beta )q^{7}+9q^{9}+\cdots\)
2112.4.a.bg	$2112$	$4$	2112.a	1.a	$1$	$2$	$2$	$124.612$	\(\Q(\sqrt{97}) \)	None	✓				33.4.a.c	$1$	$1$	\(0\)	\(-6\)	\(14\)	\(-24\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-3q^{3}+(7-\beta )q^{5}+(-12-2\beta )q^{7}+\cdots\)
2112.4.a.bh	$2112$	$4$	2112.a	1.a	$1$	$2$	$2$	$124.612$	\(\Q(\sqrt{33}) \)	None	✓				33.4.a.d	$1$	$1$	\(0\)	\(6\)	\(-16\)	\(-2\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+3q^{3}+(-8-2\beta )q^{5}+(-1-\beta )q^{7}+\cdots\)
2112.4.a.bi	$2112$	$4$	2112.a	1.a	$1$	$2$	$2$	$124.612$	\(\Q(\sqrt{97}) \)	None	✓				66.4.a.c	$1$	$0$	\(0\)	\(6\)	\(-10\)	\(2\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+3q^{3}+(-5-\beta )q^{5}+(1+3\beta )q^{7}+\cdots\)
2112.4.a.bj	$2112$	$4$	2112.a	1.a	$1$	$2$	$2$	$124.612$	\(\Q(\sqrt{73}) \)	None	✓				1056.4.a.c	$1$	$1$	\(0\)	\(6\)	\(-6\)	\(16\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+3q^{3}+(-3-\beta )q^{5}+(8+2\beta )q^{7}+\cdots\)
2112.4.a.bk	$2112$	$4$	2112.a	1.a	$1$	$2$	$2$	$124.612$	\(\Q(\sqrt{185}) \)	None	✓				264.4.a.g	$1$	$0$	\(0\)	\(6\)	\(6\)	\(-22\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+3q^{3}+(3+\beta )q^{5}+(-11+\beta )q^{7}+\cdots\)
2112.4.a.bl	$2112$	$4$	2112.a	1.a	$1$	$2$	$2$	$124.612$	\(\Q(\sqrt{17}) \)	None	✓				264.4.a.e	$1$	$1$	\(0\)	\(6\)	\(6\)	\(10\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+3q^{3}+(3+\beta )q^{5}+(5+\beta )q^{7}+9q^{9}+\cdots\)
2112.4.a.bm	$2112$	$4$	2112.a	1.a	$1$	$2$	$2$	$124.612$	\(\Q(\sqrt{137}) \)	None	✓				264.4.a.f	$1$	$0$	\(0\)	\(6\)	\(6\)	\(16\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+3q^{3}+(3+\beta )q^{5}+(8+2\beta )q^{7}+9q^{9}+\cdots\)
2112.4.a.bn	$2112$	$4$	2112.a	1.a	$1$	$2$	$2$	$124.612$	\(\Q(\sqrt{97}) \)	None	✓				33.4.a.c	$1$	$0$	\(0\)	\(6\)	\(14\)	\(24\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+3q^{3}+(7-\beta )q^{5}+(12+2\beta )q^{7}+9q^{9}+\cdots\)
2112.4.a.bo	$2112$	$4$	2112.a	1.a	$1$	$3$	$3$	$124.612$	3.3.142161.1	None	✓				264.4.a.h	$1$	$1$	\(0\)	\(-9\)	\(-4\)	\(12\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-3q^{3}+(-1+\beta _{1})q^{5}+(4-\beta _{2})q^{7}+\cdots\)
2112.4.a.bp	$2112$	$4$	2112.a	1.a	$1$	$3$	$3$	$124.612$	3.3.123209.1	None	✓				264.4.a.i	$1$	$0$	\(0\)	\(-9\)	\(-4\)	\(28\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-3q^{3}+(-1+\beta _{1})q^{5}+(10+\beta _{1}+\beta _{2})q^{7}+\cdots\)
2112.4.a.bq	$2112$	$4$	2112.a	1.a	$1$	$3$	$3$	$124.612$	3.3.91253.1	None	✓				1056.4.a.g	$1$	$1$	\(0\)	\(-9\)	\(-2\)	\(-8\)		$-$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-3q^{3}+(-1-\beta _{1})q^{5}+(-3-\beta _{1}+\cdots)q^{7}+\cdots\)
2112.4.a.br	$2112$	$4$	2112.a	1.a	$1$	$3$	$3$	$124.612$	3.3.3957.1	None	✓				1056.4.a.f	$1$	$1$	\(0\)	\(-9\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-3q^{3}+\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+9q^{9}+\cdots\)
2112.4.a.bs	$2112$	$4$	2112.a	1.a	$1$	$3$	$3$	$124.612$	3.3.18201.1	None	✓				1056.4.a.e	$1$	$0$	\(0\)	\(-9\)	\(4\)	\(-2\)		$-$	$+$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q-3q^{3}+(1-\beta _{2})q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
2112.4.a.bt	$2112$	$4$	2112.a	1.a	$1$	$3$	$3$	$124.612$	3.3.123209.1	None	✓				264.4.a.i	$1$	$1$	\(0\)	\(9\)	\(-4\)	\(-28\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+3q^{3}+(-1+\beta _{1})q^{5}+(-10-\beta _{1}+\cdots)q^{7}+\cdots\)
2112.4.a.bu	$2112$	$4$	2112.a	1.a	$1$	$3$	$3$	$124.612$	3.3.142161.1	None	✓				264.4.a.h	$1$	$0$	\(0\)	\(9\)	\(-4\)	\(-12\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+3q^{3}+(-1+\beta _{1})q^{5}+(-4+\beta _{2})q^{7}+\cdots\)
2112.4.a.bv	$2112$	$4$	2112.a	1.a	$1$	$3$	$3$	$124.612$	3.3.91253.1	None	✓				1056.4.a.g	$1$	$1$	\(0\)	\(9\)	\(-2\)	\(8\)		$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+3q^{3}+(-1-\beta _{1})q^{5}+(3+\beta _{1})q^{7}+\cdots\)
2112.4.a.bw	$2112$	$4$	2112.a	1.a	$1$	$3$	$3$	$124.612$	3.3.3957.1	None	✓				1056.4.a.f	$1$	$1$	\(0\)	\(9\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+3q^{3}+\beta _{1}q^{5}+(1-\beta _{2})q^{7}+9q^{9}+\cdots\)
2112.4.a.bx	$2112$	$4$	2112.a	1.a	$1$	$3$	$3$	$124.612$	3.3.18201.1	None	✓				1056.4.a.e	$1$	$0$	\(0\)	\(9\)	\(4\)	\(2\)		$-$	$-$	$+$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q+3q^{3}+(1-\beta _{2})q^{5}+(1+\beta _{2})q^{7}+9q^{9}+\cdots\)
2112.4.a.by	$2112$	$4$	2112.a	1.a	$1$	$4$	$4$	$124.612$	4.4.7338933.1	None	✓		✓		1056.4.a.l	$1$	$1$	\(0\)	\(-12\)	\(0\)	\(12\)		$+$	$+$	$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q-3q^{3}-\beta _{1}q^{5}+(3+\beta _{2})q^{7}+9q^{9}+\cdots\)
2112.4.a.bz	$2112$	$4$	2112.a	1.a	$1$	$4$	$4$	$124.612$	4.4.4336977.1	None	✓				1056.4.a.k	$1$	$0$	\(0\)	\(-12\)	\(10\)	\(-2\)		$+$	$+$	$+$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q-3q^{3}+(2-\beta _{1})q^{5}+\beta _{3}q^{7}+9q^{9}+\cdots\)
2112.4.a.ca	$2112$	$4$	2112.a	1.a	$1$	$4$	$4$	$124.612$	4.4.7338933.1	None	✓		✓		1056.4.a.l	$1$	$1$	\(0\)	\(12\)	\(0\)	\(-12\)		$+$	$-$	$+$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+3q^{3}-\beta _{1}q^{5}+(-3-\beta _{2})q^{7}+9q^{9}+\cdots\)
2112.4.a.cb	$2112$	$4$	2112.a	1.a	$1$	$4$	$4$	$124.612$	4.4.4336977.1	None	✓				1056.4.a.k	$1$	$0$	\(0\)	\(12\)	\(10\)	\(2\)		$+$	$-$	$-$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q+3q^{3}+(2-\beta _{1})q^{5}-\beta _{3}q^{7}+9q^{9}+\cdots\)
2112.4.a.cc	$2112$	$4$	2112.a	1.a	$1$	$5$	$5$	$124.612$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓		✓		1056.4.a.p	$1$	$0$	\(0\)	\(-15\)	\(-6\)	\(12\)		$-$	$+$	$-$	$+$	$2^{8}$	$\mathrm{SU}(2)$	\(q-3q^{3}+(-1-\beta _{1})q^{5}+(2-\beta _{2})q^{7}+\cdots\)
2112.4.a.cd	$2112$	$4$	2112.a	1.a	$1$	$5$	$5$	$124.612$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓		✓		1056.4.a.o	$1$	$0$	\(0\)	\(-15\)	\(10\)	\(12\)		$+$	$+$	$+$	$+$	$2^{7}$	$\mathrm{SU}(2)$	\(q-3q^{3}+(2+\beta _{1})q^{5}+(2+\beta _{2})q^{7}+9q^{9}+\cdots\)
2112.4.a.ce	$2112$	$4$	2112.a	1.a	$1$	$5$	$5$	$124.612$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓		✓		1056.4.a.p	$1$	$0$	\(0\)	\(15\)	\(-6\)	\(-12\)		$-$	$-$	$+$	$+$	$2^{8}$	$\mathrm{SU}(2)$	\(q+3q^{3}+(-1-\beta _{1})q^{5}+(-2+\beta _{2}+\cdots)q^{7}+\cdots\)
2112.4.a.cf	$2112$	$4$	2112.a	1.a	$1$	$5$	$5$	$124.612$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓		✓		1056.4.a.o	$1$	$0$	\(0\)	\(15\)	\(10\)	\(-12\)		$+$	$-$	$-$	$+$	$2^{7}$	$\mathrm{SU}(2)$	\(q+3q^{3}+(2+\beta _{1})q^{5}+(-2-\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2112))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2112)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 14}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(352))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(528))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(704))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(1056))\)\(^{\oplus 2}\)